Challenge: Calculating Coordinates Using Celestial Navigation

[wintz50]

I am needing to figure out coordinates using the following celestial navigation info. Can someone figure the coordinates out using this info? It would be a great help.


Here’s all the data you need:

Sidereal Hour Angle Mirfak = 308°43'21.0"
Declination Mirfak = N 49°53'48.6"

Sidereal Hour Angle Formalhaut = 15°25'52.5"
Declination Formalhaut = S 29°33'38.9"

Sidereal Hour Angle Alphecca = 126°12'42.0"
Declination Alphecca = N 26°40'55.9"

Greenwich Hour Angle Aries 0400 hours UT Aug 15 2010 = 23°27'48.0"
Greenwich Hour Angle Aries 0410 hours UT Aug 15 2010 = 25°58'12.0"

The following observations were made Aug. 15, 2010 Universal Time

Mirfak was observed at 04h01m32s UT and the reduced observation is
Ho = 17°43’ 26.61”

Formalhaut was observed at 04h04m20s UT and the reduced observation is
Ho = 11° 21’ 25.23”

Alphecca was observed at 04h06m55s UT and the reduced observation is
Ho = 31° 57’ 30.95”

[steve_hendry]

You're somewhere in this neighborhood:


U.S. Naval Observatory
Astronomical Applications Department


Celestial Navigation Data


Celestial Navigation Data for 2010 Aug 15 at 4:01:32 UT

For Assumed Position: Latitude N 40 00.0
Longitude W 79 00.0

Almanac Data | Altitude Corrections
Object GHA Dec Hc Zn | Refr SD PA Sum
o ' o ' o ' o | ' ' ' '
JUPITER 20 53.5 S 0 21.4 +23 37.3 112.1 | -2.3 0.4 0.0 -1.8
ALIOTH 190 13.5 N55 54.3 +22 08.3 325.7 | -2.4 0.0 0.0 -2.4
ALKAID 176 51.4 N49 15.8 +24 45.2 314.6 | -2.1 0.0 0.0 -2.1
ALPHECCA 150 03.5 N26 40.9 +30 43.1 280.6 | -1.7 0.0 0.0 -1.7
ALPHERAT 21 36.2 N29 09.1 +42 20.7 84.5 | -1.1 0.0 0.0 -1.1
ALTAIR 86 00.8 N 8 54.0 +58 16.6 193.3 | -0.6 0.0 0.0 -0.6
ANTARES 136 19.5 S26 27.4 + 4 48.7 229.1 | -9.9 0.0 0.0 -9.9
ARCTURUS 169 48.5 N19 07.7 +11 33.7 285.4 | -4.7 0.0 0.0 -4.7
CAPELLA 304 28.5 N46 00.4 + 5 07.5 29.8 | -9.4 0.0 0.0 -9.4
DENEB 73 23.3 N45 19.3 +83 16.2 35.9 | -0.1 0.0 0.0 -0.1
DIPHDA 12 48.5 S17 55.4 + 5 32.0 119.0 | -8.9 0.0 0.0 -8.9
DUBHE 217 45.4 N61 41.7 +17 01.6 340.9 | -3.2 0.0 0.0 -3.2
ELTANIN 114 37.6 N51 29.5 +62 57.5 307.1 | -0.5 0.0 0.0 -0.5
ENIF 57 39.6 N 9 55.6 +54 27.3 141.9 | -0.7 0.0 0.0 -0.7
FOMALHAU 39 16.7 S29 33.7 +11 16.0 145.5 | -4.8 0.0 0.0 -4.8
HAMAL 351 53.8 N23 30.8 +16 58.5 73.2 | -3.2 0.0 0.0 -3.2
KAUS AUS 107 37.0 S34 22.8 +11 04.3 203.8 | -4.9 0.0 0.0 -4.9
KOCHAB 161 10.7 N74 07.0 +40 18.0 339.2 | -1.2 0.0 0.0 -1.2
MARKAB 37 30.9 N15 15.9 +46 17.5 112.4 | -0.9 0.0 0.0 -0.9
MIRFAK 332 34.2 N49 53.8 +20 36.9 41.3 | -2.6 0.0 0.0 -2.6
NUNKI 99 51.4 S26 16.9 +20 55.8 200.0 | -2.6 0.0 0.0 -2.6
RASALHAG 119 59.0 N12 33.3 +44 45.8 244.4 | -1.0 0.0 0.0 -1.0
SABIK 126 05.6 S15 44.3 +19 07.5 228.3 | -2.8 0.0 0.0 -2.8
SCHEDAR 13 33.4 N56 35.7 +45 23.3 45.5 | -1.0 0.0 0.0 -1.0
SHAULA 120 15.3 S37 06.8 + 4 05.7 211.8 | -11.1 0.0 0.0 -11.1
VEGA 104 30.9 N38 47.8 +70 18.9 274.7 | -0.4 0.0 0.0 -0.4
POLARIS 342 34.4 N89 18.4 +39 55.1 0.9 | -1.2 0.0 0.0 -1.2
ARIES 23 50.8

Back to form

[steve_hendry]

Hmm. Formatting didn't do well. Got that output by trying test positions at

Celestial Navigation Data for Assumed Position and Time — Naval Oceanography Portal

[wintz50]

Interesting, but I need really close coords using info from my first post..I am looking for latitude and longitude coords down to the foot.

[hellosailor]

If those are sextant observations, a position within two MILES would be considered typical accuracy and two TENTHS of a mile would be considered as good as it gets. Asking for a position within the foot might make some sense if you started out with a full-fledged fixed observatory, but it ain't gonna from a boat, or even on land with just a sextant.

I've never seen a set of sightings that didn't include an AP to start with.

[wintz50]

Here is where this question is coming from.


GC2DFYA Celestial Navigation WV part 1 (Unknown Cache) in West Virginia, United States created by bodybager

The listingd posted coords are N 38° 24.619 W 082° 21.936 . I am assuming that the final coords are someplace within a couple miles from there.

[ad_astra]

Seeing as how it's a challenge to figure out, I don't think we should do the work for you. I will tell you HOW to solve it, but the actual solution is left as an exercise to the reader (because you should earn the right to find the listed geocache, and hopefully learn something, rather than learning how to beg for answers on the internet from those that do).

So you have the stars in question and their hour angles. And you have an assumed position on earth. And the time of the observations.

Step 1. Get the expected azimuth and altitudes (for instance using the USNO calculator) for each star at the time it was observed from the assumed position. You COULD do this step by hand based on the positions provided.
Step 2. Calculate the difference in altitude between the observed altitude and predicted altitude at the time of observation.
Step 3. Now this gets tricky with plotting. What I would do is print out a grid with y=latitude and x=longitude*cos([assumed]latitude). The y spacing will be closer than the x spacing.
Step 4. The center of your grid is your original assumed position. At the azimuth of the observed star, draw a line the number of units of latitude your observed alt is different from computed. Draw a line perpendicular to this line. The perpendicular line is your first line of position.
Step 5. Draw a line of position for the remaining two stars repeating step 4.
Step 6. Find the intercept between the three lines of position. This is your fix. (i.e. the location).

Good luck!

[hellosailor]

I'd throw it into my Palm, where the inexpensive "Navigation" suite by John Manson will crunch it right dow. But...like most marine navigation it needs input in DD.MMmm format not DD.MM.SSss format. Won't give you "foot" accuracy because celestial nav isn't intended for that. Engineers may use DD.MMmmmmm and similar formats, but celestial navigators just don't.

I'm not that motivated to do all the conversions. Especially given the amount of missing information, i.e. AP, index error, eye height...all the usual things needed in sight reduction.

Considering that your general goal is a point in WV, you should be aware that atmospheric distortions pretty much ensure that IF the original poster used celestial to get that position, it will be accurate within two miles--at best.

If they've just used a bogus set of numbers and run them backward from the true lat/lon...then you'll find the cache. Maybe.

There are plenty of other software products, for PDAs and PCs, that will also run the sights for you.

[Bodybager]

Originally Posted by ad_astra

Seeing as how it's a challenge to figure out, I don't think we should do the work for you. I will tell you HOW to solve it, but the actual solution is left as an exercise to the reader (because you should earn the right to find the listed geocache, and hopefully learn something, rather than learning how to beg for answers on the internet from those that do).

So you have the stars in question and their hour angles. And you have an assumed position on earth. And the time of the observations.
...
Good luck!

Well said! The whole purpose of this challenge is to test the ability to calculate Hc and plot a fix. The only difference is that in this challenge, you have to calculate Hc to a few more digits of precision than you would in real navigation, and you have to plot at a larger scale to resolve the fix to the necessary precision.

Originally Posted by wintz50

The listingd posted coords are N 38° 24.619 W 082° 21.936 . I am assuming that the final coords are someplace within a couple miles from there.

You're absolutely right.

Originally Posted by hellosailor

If those are sextant observations, a position within two MILES would be considered typical accuracy and two TENTHS of a mile would be considered as good as it gets. Asking for a position within the foot might make some sense if you started out with a full-fledged fixed observatory, but it ain't gonna from a boat, or even on land with just a sextant.

Right. These are artificial observations. Real observations would not be that accurate. However, I'd like to take this time to brag that I have calculated a terrestrial fix within 100 feet using a very accurate theodolite. When SA was on, that was as good as uncorrected GPS.

Originally Posted by hellosailor

I've never seen a set of sightings that didn't include an AP to start with.

You can use any assumed position you want, but the one given in the challenge is a great place to start. As previously said, it's within a few miles of the cache.

These are not actual sextant observations. They are computed altitudes at the actual location of the cache (and they are computed with the data given in the challenge, so other almanac data will probably put you in error a tenth of a mile or so). So they are artificially derived, but perfectly suitable for finding the coordinates of the cache. In fact, since the altitudes are computed to the nearest 0°0'0.01" you can determine the position to the nearest 1 foot. I plotted a fix at 1"=100 foot scale using this data and scaled the fix to within 6' of the true coordinates. This would only be possible with artificial observations.

Originally Posted by hellosailor

I'd throw it into my Palm, where the inexpensive "Navigation" suite by John Manson will crunch it right dow. But...like most marine navigation it needs input in DD.MMmm format not DD.MM.SSss format. Won't give you "foot" accuracy because celestial nav isn't intended for that. Engineers may use DD.MMmmmmm and similar formats, but celestial navigators just don't.

The programs written for celestial navigation often include their own almanac and only resolve angles to the nearest 0°0.1' at best. This will not do for this challenge. You MUST use the ephemeris data provided and calculate Hc to the nearest 0°0'0.01" (or 0.0001 minutes or 0.000001 degrees)

Originally Posted by hellosailor

I'm not that motivated to do all the conversions. Especially given the amount of missing information, i.e. AP, index error, eye height...all the usual things needed in sight reduction. Considering that your general goal is a point in WV, you should be aware that atmospheric distortions pretty much ensure that IF the original poster used celestial to get that position, it will be accurate within two miles--at best.

Ho is provided, not Hs. No correction is necessary.

Originally Posted by hellosailor

If they've just used a bogus set of numbers and run them backward from the true lat/lon...then you'll find the cache. Maybe.

There are plenty of other software products, for PDAs and PCs, that will also run the sights for you.

The ephemeris data is not bogus, but the altitudes were computed by running back from the real Lat/Lon. But as said before, no program out there will calculate this to the accuracy you need to find it. You MUST compute Hc using a scientific calculator or Excel or something that will not round off to the nearest tenth of a minute, and it is crucial that you use the almanac data provided because other almanacs might round differently here and there and that can mean being off a thousand feet.

I'm not surprised that geocachers are asking for someone to solve this puzzle for them. I am however surprised that so far, not a single person has computed the position in spite of having all the data and even all the formulas right there on that page. But I am certainly glad that no one calculated it for them and handed over the coordinates!

[wintz50]

well, after browsing all of that, i think i will just solve this puzzle the way 99% of puzzle caches are solved.

good luck!

[wintz50]

Ok I found it. I had to just rely on my gpsr's celestial navigation to find it though. I did find the stars though..